The present invention relates to a process for cracking an olefin-rich hydrocarbon feedstock which is selective towards light olefins in the effluent. In particular, olefinic feedstocks from refineries or petrochemical plants can be converted selectively so as to redistribute the olefin content of the feedstock in the resultant effluent. The present invention further relates to a process for desulphurising such a feedstock which includes sulphur-containing hydrocarbon compounds as impurities.